The baby, born on Dec. 25 by a surrogate mother in California, is called Zachary and weighs 7 pounds, 15 ounces. The couple didn’t provide details about the surrogacy arrangements.
“We are overwhelmed with happiness and joy at this very special moment,” the two men said in a joint statement, quoted by the magazine.
“Zachary is healthy and doing really well, and we are very proud and happy parents.”
Sir Elton John and David Furnish, a Canadian filmmaker, were married in 2005.
Last year, the singer had attempted to adopt 14-month-old boy after a visit to an orphanage in Ukraine but the regulations of the country didn’t allow adoption by same-sex parents.
He had confided at the time that David Furnish had always wanted to adopt a child while he had viewed parenthood as incompatible with his lifestyle. But it was then that he admitted that the Ukrainian boy changed his mind.
Elton John, 62, and David Furnish, 48, have been together for 12 years and were married in 2005 in England, on the same day that the British law recognized gay marriages.